Microsoft has released public updates for its collection of Project Server editions — Project Server 2010, 2013, and 2016 — as well as updates for Project 2013 and 2016.
In her detailed rundown on the releases Support Escalation Engineer Suzanne Sylliaasen notes a few caveats:

• The updates for 2013 absolutely won’t work if Service Pack 1 hasn’t been installed on components or language packs. This also means, she points out, that release to manufacture (RTM) is no longer supported.’
• 2010 products have a “hard requirement” for Service Pack 2, including for the language packs. An SP1-patched 2010 system with no SP2 is no longer supported.
• Project Server 2016 has only a single patch; but there’s also a patch for SharePoint Server 2016; and both parts are needed before the config wizard will work.

As always, Microsoft strongly recommends testing updates in your non-production environment before you go whole-hog in your working environment.